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→Controlled gate to construct the Bell state
===Controlled gate to construct the Bell state===
===Controlled gate to construct the Bell state受控门构造钟态===
<math>\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)_A</math> and <math>|0\rangle_B</math>
<math>\frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)_A</math> and <math>|0\rangle_B</math>
[[Quantum logic gate|Controlled gates]] act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the [[controlled NOT gate]] (or CNOT or cX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is <math>|1\rangle</math>, and otherwise leaves it unchanged. With respect to the unentangled product basis <math>\{|00\rangle</math>, <math>|01\rangle</math>, <math>|10\rangle</math>, <math>|11\rangle\}</math>, it maps the basis states as follows:
[[Quantum logic gate|Controlled gates]] act on 2 or more qubits, where one or more qubits act as a control for some specified operation. In particular, the [[controlled NOT gate]] (or CNOT or cX) acts on 2 qubits, and performs the NOT operation on the second qubit only when the first qubit is <math>|1\rangle</math>, and otherwise leaves it unchanged. With respect to the unentangled product basis <math>\{|00\rangle</math>, <math>|01\rangle</math>, <math>|10\rangle</math>, <math>|11\rangle\}</math>, it maps the basis states as follows:
[[量子逻辑门|受控门]]作用于2个或多个量子比特，其中一个或多个量子比特作为某些特定操作的控制。具体而言，[[controlled NOT gate]]（或CNOT或cX）作用于2个量子位，并且仅当第一个量子位为<math>| 1\rangle</math>时才对第二个量子位执行NOT操作，否则保持不变。对于无缠结的产品基<math>\{00\rangle</math>、<math>|01\rangle</math>、<math>|10\rangle</math>、<math>|11\rangle\}</math>，它将基状态映射如下：
After applying C<sub>NOT</sub>, the output is the <math>|\Phi^+\rangle</math> Bell State: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>.
After applying C<sub>NOT</sub>, the output is the <math>|\Phi^+\rangle</math> Bell State: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>.
应用 c < sub > NOT </sub > 后，输出为 < math > | Phi ^ + rangle </math > Bell State: < math > frac {1}{ sqrt {2}(| 00 rangle + | 11 rangle) </math > 。
应用 C< sub > NOT </sub > 后，输出为 < math > | Phi ^ + rangle </math > 贝尔态: < math > frac {1}{ sqrt {2}(| 00 rangle + | 11 rangle) </math > 。
:<math> | 0 0 \rangle \mapsto | 0 0 \rangle </math>
:<math> | 0 0 \rangle \mapsto | 0 0 \rangle </math>
A common application of the C<sub>NOT</sub> gate is to maximally entangle two qubits into the <math>|\Phi^+\rangle</math> [[Bell state]]. To construct <math>|\Phi^+\rangle</math>, the inputs A (control) and B (target) to the C<sub>NOT</sub> gate are:
A common application of the C<sub>NOT</sub> gate is to maximally entangle two qubits into the <math>|\Phi^+\rangle</math> [[Bell state]]. To construct <math>|\Phi^+\rangle</math>, the inputs A (control) and B (target) to the C<sub>NOT</sub> gate are:
C<sub>NOT</sub>门的一个常见应用是最大限度地将两个量子位纠缠到<math>|\Phi^+\rangle</math>[[Bell state]]。要构造<math>|\Phi^+\rangle</math>，到C<sub>NOT</sub>门的输入A（控制）和B（目标）是：
Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation. A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably.
Quantum entanglement also allows multiple states (such as the Bell state mentioned above) to be acted on simultaneously, unlike classical bits that can only have one value at a time. Entanglement is a necessary ingredient of any quantum computation that cannot be done efficiently on a classical computer. Many of the successes of quantum computation and communication, such as quantum teleportation and superdense coding, make use of entanglement, suggesting that entanglement is a resource that is unique to quantum computation. A major hurdle facing quantum computing, as of 2018, in its quest to surpass classical digital computing, is noise in quantum gates that limits the size of quantum circuits that can be executed reliably.
After applying C<sub>NOT</sub>, the output is the <math>|\Phi^+\rangle</math> Bell State: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>.
After applying C<sub>NOT</sub>, the output is the <math>|\Phi^+\rangle</math> Bell State: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>.
应用C<sub>NOT</sub>之后，输出为 <math>|\Phi^+\rangle</math> 贝尔态: <math>\frac{1}{\sqrt{2}}(|00\rangle + |11\rangle)</math>。
===Applications应用===
===Applications应用===